The result was The Young Ones; the show was written by a very youthful Ben Elton, Rik Mayall and Mayall's then-girlfriend Lise Mayer, all of whom remain successful figures in the comedy industry. Although it was initially ignored by critics, the programme soon proved itself a favourite among school children, and the BBC commissioned a second series. As well as producing, Jackson directed many episodes of the series, with Geoff Posner, now also a successful producer, helming the rest.

He followed The Young Ones with Happy Families, which was written by Ben Elton alone and featured many of the same actors, including its star Adrian Edmondson. It wasn't received terribly well at the time by many people, who expected another Young Ones. Despite this, its many styles of pastiche and parody indicate Jackson's directorial skills, even if he allows certain people to unbalance the show by horrible overacting (notably an unbelievably hammy Stephen Fry as the local doctor).

Jackson also worked as a director on two other sitcoms in the 1980s: Girls on Top, which starred Dawn French, Jennifer Saunders, Ruby Wax and Tracey Ullman, and on Filthy, Rich and Catflap, another venture reuniting Edmondson, Mayall and Planer. Girls on Top proved very important in helping launch the careers of French, Saunders and Wax (Ullman was already well-known and jumped ship to America after 8 episodes), while Filthy was less successful but led Edmondson and Mayall towards their highly lucrative Bottom characters.

In 1988, Jackson brought science fiction situation comedyRed Dwarf to British TV screens. Its writers Rob Grant and Doug Naylor had spent 5 years attempting to get it made in the face of industry scepticism about science fiction, and doubts over whether science fiction fans had a sense of humour. Grant and Naylor knew Paul Jackson since they had all worked on satirical puppet show Spitting Image, and the three of them spent some time thinking up a suitable project; without Jackson's reputation and this connection it is unlikely to have made it to the screens.

As with his other sitcoms, Red Dwarf tells the story of a bunch of people stuck in a small space, this time not a house or apartment but a spaceship, and not through poverty but as a result of an accident that leaves them stranded in the distant future, far from Earth. As with The Young Ones, the stars of Red Dwarf were not professional actors, but were drawn largely from the field of stand-up comedy (Chris Barrie was an impressionist, Craig Charles a comic performance poet and Norman Lovett a respected stand-up). Jackson left the show after three series, and Grant and Naylor took over production duties. The result is an enormously popular show, and like The Young Ones it has a fanatical cult following.

He followed this with Heil, Honey I'm Home, an early attempt at original programming by satellite channel Sky One (which was better known for running American imports such as Beverly Hills, 90210). The show was evidently intended as a succes de scandale, but its parody of ancient American sitcoms such as the Honeymooners was close to a one-joke idea and (from the little I've seen) not a very funny one joke. The show was universally condemned as tasteless (although similar material had featured in very successful films like The Producers and To Be or Not to Be) and Heil, Honey died a rapid and ignominious death. Only one episode was ever broadcast.

In the 1990s, Jackson worked more as an television executive, with less creative control over individual shows. He moved to Carlton TV, and helped prepare the bid that won them the franchise for weekday independent television in the London area in 1991. When they began broadcasting in 1993, he was director of programmes and he later became managing director at Carlton (the channel initially had a very bad reputation for the low quality of its output and for axing acclaimed serious shows such as documentary This Week).